We can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
In this case, the given point is (-3, 4) and the slope is -5/3. Plugging these values into the point-slope form, we get:
y - 4 = (-5/3)(x - (-3))
Simplifying further, we have:
y - 4 = (-5/3)(x + 3)
To convert it into slope-intercept form (y = mx + b), we can distribute the -5/3:
y - 4 = (-5/3)x - 5
Then, we can isolate y by adding 4 to both sides:
y = (-5/3)x - 1
So, the slope-intercept form of the equation of the line is y = (-5/3)x - 1.